If the range of a set of data is 20, find a rough approximation to the standard deviation of the data set.

The variance or standard deviation of how much variance as well as dispersion there is in a group of numbers. A smaller standard deviation suggests that information is grouped around the mean, whereas a largestandard deviationshows that observations are more dispersed.

In absence of the standard deviation value, we use the range to find an approximated value of standard deviation. We know that majority of the observations should fall within ±3 standard deviations from the mean and we also know that the standard deviation cannot be more than 1/4^th of the range. Therefore, we use the following formula to estimate the Standard deviation.

$$\begin{gathered} s=\frac{Range}{4} \\ s=\frac{20}{4} \\ s=5 \end{gathered}$$

Therefore, the rough approximation of standard deviation is 5.